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Application of the Monomer Reactivity Ratios to the Kinetic-Model Discrimination and the Solvent-Effect Determinationfor the Styrene/Acrylonitrile Monomer System
ANDRZEJ KAIM
Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland
Received 10 March 1999; accepted 6 December 1999
ABSTRACT: The impact of reactivity ratios determined with the Nelder and Mead
simplex method on the kinetic-model discrimination and the solvent-effect determina-
tion for the styrene/acrylonitrile monomer system was investigated. For the monomer
system, the penultimate unit effect was inversely proportional to the polarity of the
solvent: acetonitrile N , N -dimethylformamide methyl ethyl ketone toluene.
Quantitatively, the penultimate unit effect could be correlated with an absolute value
of the difference between the standard deviation of the reactivity ratios determined for
the terminal and penultimate models. By application of the F test, the penultimate
model was justified for copolymerization in toluene. The conclusion was less certain for
polymerization in methyl ethyl ketone. With a scanning procedure based on the simplex
method, it was found that an equivalent representation of the copolymer-composition
data could be achieved with multiple sets of penultimate-model reactivity ratios.
However, the relationship between the triad-sequence distribution and copolymer
composition depended on the reactivity-ratio set chosen for the microstructure deter-
mination. The microstructure calculated with the penultimate-model reactivity ratios
determined with the simplex method from the initial guess (r11 r1, r21 1/ r2, r22 r2,
r12 1/ r1) did not obey the general “bootstrap effect” rule. This observation still
requires some theoretical interpretation. © 2000 John Wiley & Sons, Inc. J Polym Sci A:
Polym Chem 38: 846–854, 2000
Keywords: styrene; acrylonitrile; radical copolymerization; reactivity ratios; solvent
effects; microstructure
INTRODUCTION
The choice of the proper kinetic model for describ-ing the composition and microstructure of copol-
ymers produced by free-radical copolymerizationhas been the subject of many investigations. For
most monomer systems, the terminal1 model suc-ceeds in describing copolymer composition interms of the monomer-feed composition (eq 1). For
example, for the styrene/methyl methacrylate
(STY-MMA) monomer system, both the terminal
and penultimate2 models (eq 2) present almost
the same perfect fit to the composition data:3,4
n d M 1d M 2
M 1 M 2
M 1r1 M 1 M 2 M 2r2 M 2 M 1
(1)
n d M 1
d M 2
1 r21
M 1r11 M 1 M 2
M 2r21 M 1 M 2
1 r12
M 2r22 M 2 M 1
M 1r12 M 2 M 1
(2)Correspondence to: A. Kaim (E-mail: [email protected].
uw.edu.pl)
Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 38, 846–854 (2000)
© 2000 John Wiley & Sons, Inc.
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where n represents the monomer ratio in the co-
polymer and [ M 1] and [ M 2] are the mole fractionsof monomer M 1 and M 2, respectively. Parameters
r1, r2, r11, r22, r21, and r12, defined in a conven-tional way, stand for the reactivity ratios of themonomers M 1 and M 2 in the terminal and penul-
timate models, respectively.Systems have been reported, however, in which
the introduction of the four-parameter penulti-mate model (also called the explicit penultimate
model2) gives an improved fit to the compositiondata over the two-parameter (terminal) model.For example, the styrene/acrylonitrile (STY-AN)
monomer system is better described5–7 with thepenultimate model than with the terminal model.
However, an examination of the rate constantof propagation and termination in the copolymer-
ization of numerous monomer systems, including the STY-MMA monomer system, as a function of
monomer composition in a feed results in the con-clusion that the terminal model fails to describethe absolute rate of the propagation for the sys-
tem.8 Despite this, the model still is used often fordescribing the composition and microstructure of
most copolymers produced by free-radical copoly-merization. As summarized recently,9 to justifythe continued use of the terminal-model composi-
tion and triad/pentad fraction equations in suchsystems, the implicit penultimate model8 has
been proposed.It is well-recognized that the perfect fit of one
or another kinetic model can be considered when
it provides simultaneously a satisfactory fit to thecomposition and the overall propagation-rate da-
ta.9 However, a question can be raised: how pow-erful are composition data in discriminating be-
tween the terminal and penultimate model forbinary copolymerization? An interesting study on
the subject was dome some time ago by Moad etal.10
Some new aspects of the present state of theart justify in my opinion a further exploration of the problem. One of them is the successful appli-
cation of the nonlinear least-squares (nlls) ap-proach based on the Nelder and Mead11 simplex
method to fit both the terminal and the penulti-mate models to the copolymer-composition data.
This method enables to estimate reactivity ratiosand related standard deviations with optionalprecision. With a scanning procedure based on
the simplex method, it has been demonstrated4,12
that the equivalent representation of the copoly-
mer composition in terms of the monomer-feed
composition can be achieved with multiple penul-
timate-model reactivity ratios. These multiplepenultimate-model reactivity ratios belong to two
different sets of parameters, Set I and Set II,resulting from two different initial guesses for r11,
r22, r21, and r12 (Guess I: r11 r21 r1, r22 r12
r22; Guess II: r11 r1, r21 1/ r2, r22 r2, r12 1/ r1) used for the nlls approach. Moreover, the
most accurate reactivity ratios were surroundedwith sets of reactivity-ratio values of equal accu-
racy. In other words, multiple sets of penulti-mate-model reactivity ratios can describe thecomposition data with the same minimal stan-
dard deviation ( ). Similar results were obtainedfor both the STY-MMA and STY-AN monomer
systems.3,4,12 Contrary to the STY-MMA system,for which the penultimate model did not yield any
significant improvement in the fit to experimentaldata when compared to the terminal model, im-
plications of the nonuniqueness in determining the penultimate-model reactivity ratios can bequite different for the system displaying a pro-
nounced penultimate unit effect (e.g., the STY- AN system). This is quite obvious, because for
examining solvent effects formulated in terms of the relation between the copolymer compositionand the monomer-feed composition (the so-called
“bootstrap effect” by Harwood13), an adequate ki-netic model and well-fitted reactivity ratios are
required.14 When one considers the nonunique-ness in determining the penultimate-model reac-
tivity ratios, the choice of the penultimate-model
reactivity ratios used for this purpose can be evenmore complicated because, by analogy with the
copolymer of STY with MMA in bulk,15 the micro-structure of the STY-AN copolymer may depend
on the choice of the r-parameter set (Set I or SetII) used for calculation.
The multiple solutions of the copolymerizationequation originate from the nonlinear calculation
methods applied in determination of the reactiv-ity ratios. If this approach is assumed to be usedwidely today, the problem of the reactivity-ratio
selection used for the description of copolymeriza-tion systems can acquire in the future an even
greater importance. There is good reason for thisexpectation because determination methods for
the terminal-model reactivity ratios based on thelinearization of the Mayo–Lewis equation1 (eq 1)have been criticized for a long time,16,17 besides
being useless for the penultimate model (eq 2). Inrecent case studies and a comprehensive litera-
ture review18–20 on the estimation of copolymer-
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T a b l e
I .
T e r m i n a l - a n d P e n u l t i m a t e - M o d e l P a r a m e t e r s f o
r t h e S t y r e n e ( M 1 ) / A c r y l o n i t r i l e ( M 2
) F r e e - R a d i c a l C o p o l y m e r i z a t i o n S y s t e m
i n T o l u e n e
( T ) , M e t h y l E t h y l K e t o n e ( M E K ) , N , N - D i m e t h y l f o r m a m i d e
( D M F ) , a n d A c e t o n i t r i l e ( A C N ) E s t i m
a t e d w i t h t h e S i m p l e x M e t h o d
P a r a m e t e r
T e r m i n a l M o d e l a
P
e n u l t i m a t e M o d e l
S e t I b
S e t I I c
T d
T
c
M E K e
D M F e
A C N d
T d
T e
M E K e
D M F e
A C N d
T d
T e
M E K e
D M F e
A C N d
r 1
0 . 3 6 9
( 0 . 4 2 3 )
0 . 3 2 8
0 . 3 3 4
0 . 2 4 0
0 . 4 8 8
( 0 . 4 8 5 )
r 2
0 . 1 2 8
( 0 . 1 1 8 )
0 . 1 0 3
0 . 0 7 8
0 . 1 1 7
0 . 0 6 5
( 0 . 0 8 1 )
r 1 1
0 . 2 5 4
( 0 . 2 4 2 )
0 . 2 2 5
( 0 . 2 4 2 )
0 . 2 5 8
( 0 . 2 8 4 )
0 . 2 0 5
( 0 . 2 2 7 )
0 . 4 2 7
( 0 . 3 2 2 )
0 . 2 0 6
0 . 2 2 0
0 . 2 4 9
0 . 2 0 0
0 . 4 4 8
r 2 2
0 . 2 5 5
( 0 . 1 3 3 )
0 . 1 2 0
( 0 . 1 0 8
0 . 0 7 1
( 0 . 0 6 3 )
0 . 1 0 9
( 0 . 1 0 5 )
0 . 0 6 0
( 0 . 0 5 2 )
0 . 2 1 9
0 . 1 9 5
0 . 0 6 6
0 . 1 0 8
0 . 0 7 1
r 2 1
0 . 4 5 9
( 0 . 5 6 6 )
0 . 5 3 2
( 0 . 5 5 9 )
0 . 4 7 0
( 0 . 5 7 0 )
0 . 3 1 5
( 0 . 4 4 0 )
0 . 6 0 3
( 0 . 6 2 1 )
2 5 . 6 3 5
1 0 7 . 5 7 2
6 . 0 1 8
6 . 1 7 8
1 7 . 6 4 8
r 1 2
0 . 0 6 0
( 0 . 1 0 9 )
0 . 0 9 5
( 0 . 1 1 9 )
0 . 0 9 9
( 0 . 1 3 2 )
0 . 1 4 2
( 0 . 1 7 5 )
0 . 0 7 7
( 0 . 1 0 5 )
1 . 0 5 5
1 . 4 3 9
1 . 1 4 4
2 . 5 7 0
1 . 7 2 7
f
0 . 0 2 4 6 0
( 0 . 0 4 9 )
0 . 0 1 9 2 8
0 . 0 1 2 4 1
0 . 0 1 7 1 8
0 . 0 0 6 2 0
( 0 . 0 5 1 )
0 . 0 0 8 1 5
( 0 . 0 2 3 )
0 . 0 1 1 0 6
0 . 0 1 0 7 7
0 . 0 1 7 7 3
0 . 0 0 5 1 9
( 0 . 0 2 0 )
0 . 0 1 2 2 9
0 . 0 0 9 7 2
0 . 0 0 7 7 2
0 . 0 1 7 8 1
0 . 0 0 6 2 1
g
0 . 0 1 6 4 5
0 . 0 0 8 2 2
0 . 0 0 1 6 4
0 . 0 0 0 5 5
0 . 0 0 0 0 1
0 . 0 1 2 3 1
0 . 0 0 9 5 6
0 . 0 0 4 6 9
0 . 0 0 0 6 3
0 . 0 0 0 0 1
p h
2
2
2
2
2
4
4
4
4
4
4
4
4
4
4
n i
1 1
1 3
1 4
1 5
1 2
1 1
1 3
1 4
1 5
1 2
1 1
1 3
1 4
1 5
1 2
F ( 9 9 . 5
% )
j
3 . 6 8
3 . 1 0
2 . 9 1
2 . 7 8
3 . 3 5
3 . 6 8
3 . 1 0
2 . 9 1
2 . 7 8
3 . 3 5
F c a l c d
k
2 8 . 3 9
9 . 1 7
1 . 6 4
0 . 3 4
1 . 1 7
1 0 . 5 2
1 3 . 2 0
7 . 9 2
0 . 3 8
0 . 0 1
V a l u e s i n p a r e n t h e s e s
c o m e f r o m
o r i g i n a l w o r k s .
a U s i n g r 1
0 . 5 a n d r
2
0 . 1 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .
b U s i n g r 1 1
r 2 1 r 1
a n d r 2 2
r 1 2
r 2 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .
c U s i n g r 1 1
r 1 , r 2 1
1 / r 2 , r 2 2
r 2 , a n d r 1 2
1 / r 1 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .
d C a l c u l a t e d w i t h d a t a
b y H i l l e t a l . 6
e C a l c u l a t e d w i t h d a t a
b y K l u m p e r m a n a n d K r a e g e r .
7
f S t a n d a r d d e v i a t i o n i s
d e fi n e d a s
i 1
n
F i e x p t l F i c a l c d
2 / n p w h e r e F
i
i s t h e m o l e f r a c t i o n o f t h e m o n o m e r M
i
e x p r e s s e d f o r t h e t e r m i n a l a n d p e n u l t i m a t e
m o d e l s i n t h e c o r r e s p o n d i
n g r e a c t i v i t y r a t i o s , n i s t h e n u m b e r o f e x p e r i m e n t a l p o i n t s , a n d p i s t h e n u m b e r
o f r p a r a m e t e r s .
g A b s o l u t e v a l u e o f t h e d i f f e r e n c e b e t w e e n t h e s t a n d a r d d e v i a t i o n o f t h e r e a c t i v i t y r a t i o s d e t e r m i n e d f o r t h e m o n o m e r s y s t e m
i n t h e s o l v e n t f o r t h e t e r m i n a l a n d
p e n u l t i m a t e m o d e l s ,
( t e r m i n a l m o d e l )
( p e n u l t i m a t e m
o d e l )
.
h N u m b e r o f r p a r a m e t e r s i n t h e k i n e t i c m o d e l .
i N u m b e r o f c o p o l y m e r
i z a t i o n e x p e r i m e n t s .
j C r i t i c a l v a l u e s o f F f o
r t h e p r o b a b i l i t y l e v e l
9 9 . 5 % ( t a k e n
f r o m
r e f . 2 8 ) .
k F
c a l c d c a l c u l a t e d a c c o r d i n g t o e q . 3 , 2
7 w h e r e M o d e l s B a n d A s
t a n d f o r t h e t e r m i n a l m o d e l a n d p e n u l t i m
a t e m o d e l , r e s p e c t i v e l y .
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ization reactivity ratios, a further extension of the
nonlinear approach is recommended and, becauseof advances in computing power, anticipated.
Therefore, the proper choice of monomer reac-tivity ratios for the kinetic-model discriminationand the solvent-effect determination in the free-
radical copolymerization of the monomer pairsdisplaying the penultimate effect can be relevant.
The aim of this article is to study the impact of reactivity ratios determined with the simplex
method on the kinetic-model discrimination andsolvent-effect determination for a monomer sys-tem, such as the STY-AN system, displaying a
penultimate effect.
EXPERIMENTAL
In this study, monomer-feed- and copolymer-com-
position data for the STY-AN system given by Hillet al.6 for toluene and acetonitrile and by Klump-erman and Kraeger7 for toluene, methyl ethyl
ketone (MEK), and N , N -dimethylformamide (DMF)were used.
Calculation procedures for the reactivity-ratiodetermination and scanning were based on the
Nelder and Mead11 simplex concept and wereused as described previously.4,12,21
RESULTS AND DISCUSSION
Penultimate Unit Effect in the Investigated Systems
Terminal- and penultimate-model reactivity ra-tios for the STY ( M 1)/AN ( M 2) monomer system in
toluene, MEK, DMF, and acetonitrile as esti-mated with the simplex method are presented in
Table I. For the penultimate model, two differentinitial guesses for the reactivity ratios (Guess I:
r11 r21 r1, r22 r12 r22; Guess II: r11 r1,r21 1/ r2, r22 r2, r12 1/ r1) led to two differentpenultimate reactivity-ratio sets, Set I and Set II.
More precisely, for all investigated systems, wideranges of penultimate-model reactivity ratios
with the same minimal standard deviation ( )were found. Multiple penultimate-model reactiv-
ity ratios in the STY-AN free-radical copolymer-ization system in bulk were the subject of myprevious article.12 Results obtained for a solution
copolymerization in acetonitrile, DMF, MEK, andtoluene were qualitatively very similar. Two-di-
mensional projections ( against rij; i, j 1,2; i
j) of the five-dimensional space (r11, r21, r22, r12, ) that resulted from the scanning experiments22
over wide ranges of the value had approxi-
mately the same shape for all the solvents, asshown schematically in Figure 1. The differences
for the investigated solvents consisted of the rel-ative position of the global and local minima (seeSet I and Set II in Table I). In addition, the
two-dimensional projections ( against rij; i, j
1,2; i j) resulted in a similar curve with one
minimum only (not shown). A comparison of the copolymerization-system
descriptions accomplished via the terminal- and
penultimate-model reactivity ratios (Table I) ispresented in Figure 2. The composition data for
all the investigated copolymerizations could bedescribed equally well with quite different sets of
the penultimate-model r parameters with veryclose standard deviations. An inspection of the
coincidence of the composition curves for the dif-ferent solvent systems revealed differences in thesignificance of the penultimate unit effect in the
solvent systems. The penultimate unit effect ap-peared to increase approximately in the following
order: acetonitrile DMF MEK toluene.Therefore, it was inversely proportional to the
polarity (expressed in Debye unit) of the solventused (3.92,23 3.82,24 2.77,25 and 0.36,26 respec-
tively). These findings led to the conclusion thatthe stronger interactions between the solvent andmonomers were less when the penultimate unit
effect was pronounced. Generally, it seems thatthe scale of the observed penultimate unit effect
depends on the solvent.
Figure 1. General picture of two-dimensional projec-
tions ( against rij; i, j 1,2; i j) of the five-dimen-
sional space (r11, r21, r22, r12, ) that resulted from the
scanning experiments22 for the STY-AN free-radical
copolymerization in toluene, MEK, DMF, and acetoni-
trile. values correspond to those for the penultimate
model given in Table I.
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Figure 2. Copolymerization diagrams for the STY/AN free-radical copolymerization
systems at 60 °C with the reactivity ratios calculated by the simplex method presented
in Table I: (a) calculated for toluene with data by Hill et al.,6 (b) calculated for toluene
with data by Klumperman and Kraeger,7 (c) calculated for MEK with data by Klump-
erman and Kraeger,7 (d) calculated for DMF with data by Klumperman and Kraeger7
[points (Œ) were generated with the penultimate-model reactivity ratios given by these
authors (r11 0.227, r22 0.105, r21 0.440, r12 0.175, 0.02163)], and (e)calculated for acetonitrile with data by Hill et al.6 } experimental points; points
generated according to eq 1 with the reactivity ratios for the terminal model; E points
generated according to eq 2 with the reactivity ratios estimated for the penultimate
model with r11 r21 r1 and r22 r12 r2 as the initial guess for the (nlls) fit (Set I);
points generated according to eq 2 with the reactivity ratios estimated for the
penultimate model with r11 r1, r21 1/ r2, r22 r2, and r12 1/ r1 as the initial guess
for the (nlls) fit (Set II).
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Klumperman and Kraeger7 also related the co-incidence of the copolymer-composition curves for
the discussed systems with the polarity of thesolvent. However, they found qualitatively, con-
trary to our results, that the copolymer-composi-tion curve for polymerization in DMF was not inagreement with the proposition. They tried to ex-
plain this exception with subtle differences in theinteractions between the electron-donor and elec-
tron-acceptor molecules present in the polymer-
ization system. In my opinion, a different expla-nation is also possible. Quantitatively, the signif-icance of the penultimate unit effect for themonomer system in the discussed solvents can be
(rigorously under certain statistical conditions)correlated with an absolute value of the difference
between the standard deviation ( ) of the reactiv-ity ratios determined for the terminal and penul-
timate models ( in Table I). According to TableI, increased in the same order as the penulti-mate unit effect (acetonitrile DMF MEK
toluene) regardless of the penultimate reactiv-ity-ratio set (Set I or Set II) taken for comparison.
Differences between the numerical values of appeared to be meaningless, but a case with the
solvent effect of DMF proved the contrary. For thereactivity ratios given by Klumperman and Krae-ger7 (r11 0.227, r22 0.105, r21 0.440, r12 0.175), the calculated standard deviation ( )was 0.02163. However, for the reactivity ratios
estimated with the simplex method from the
same experimental data (r11 0.205, r22 0.109,
r21 0.315, r12 0.142) was 0.01773 (Table I).Because the difference between the two values
was 0.0049, it is easy to distinguish on thegraphic scale [Œ in Fig. 2(d)]. This example showsagain how high the level of accuracy in the deter-
mination of reactivity ratios must be to concludefrom composition data the correct kinetic-model
discrimination.Hill et al.27 proposed the application of the
statistical F test28 to prove if the use of the four-parameter (penultimate) model is justifiable forfitting the composition data. In other words, with
this test a justness of the use of a higher ordermodel can be verified. According to the proposal,
the test is based on the ratio F of the residualsums of the squares ( 2) of Models A and B, where
Model B (terminal) is a special case of Model A (penultimate) (eq 3):
F B
2 A
2 / p A p B
A2 / n p A
(3)
Figure 3. STY ( M 1) -centered triad fractions for the
STY/AN free-radical copolymerization estimated withthe reactivity ratios for the terminal model (full points)
and penultimate model (blank points) with r11 r21 r1 and r22 r12 r2 as the initial guess for the (nlls)
fit (Set I). , ƒ toluene with data by Hill et al.;6 F, E)
toluene with data by Klumperman and Kraeger;7 ‹,
MEK with data by Klumperman and Kraeger;7 },
DMF with data by Klumperman and Kraeger;7 Œ,
‚ acetonitrile with data by Hill et al.6
Figure 2. (Continued from the previous page)
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where p A and pB are the numbers of the param-
eters for each model and n is the number of copo-lymerization experiments. Calculated F calcd ratios
and critical values of F for the probability level (
99.5%) are shown in Table I. Results showed
that from a statistical point of view, the applica-
tion of the penultimate model for the description
of STY-AN copolymerization in toluene ( F calcd F (99.5%)) is justified. For copolymerization in
MEK, the result of the test was not certain anddepended on the penultimate reactivity-ratio set
(Set I or Set II) taken for consideration. However,
Figure 4. STY ( M 1) -centered triad fractions for the STY/AN free-radical copolymer-
ization estimated with the reactivity ratios for the penultimate model with r11 r1, r21 1/ r2, r22 r2, and r12 1/ r1 as the initial guess for the (nlls) fit (Set II): (a) f M 1 M 1 M 1
triad fraction, (b) f M 2 M 1 M 2 triad fraction, and (c) f M 2 M 1 M 1 triad fraction. ƒ toluene
with data by Hill et al.;6 E toluene with data by Klumperman and Kraeger;7 ‹
MEK with data by Klumperman and Kraeger;7 } DMF with data by Klumperman
and Kraeger;7 Œ acetonitrile with data by Hill et al.6
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for copolymerization in DMF and acetonitrile so-
lutions, the penultimate model should be rejectedbecause it does nor provide a better fit to experi-
mental data in comparison with the terminaldata. Note that the F test results were in generalagreement with the conclusion that the penulti-
mate unit effect can be correlated with an abso-lute value of the difference between the standard
deviation of the reactivity ratios determined forthe terminal and penultimate models. Other con-
sequences of treating the same experimental databy different models with a different number of parameters have been discussed previously.4,21
Microstructure of the Copolymers
A comparison of the STY ( M 1) -centered triad
fractions f M 1 M 1 M 1, f M 2 M 1 M 1, and f M 2 M 1 M 2 for theSTY-AN free-radical copolymers estimated with
reactivity ratios for the terminal and penultimatemodels (Set I in Table I) is presented in Figure 3.In the curves for the STY-AN free-radical copoly-
merization in acetonitrile, DMF, MEK, and tolu-ene, the bootstrap effect is observed; that is, the
relationship between the triad-sequence distribu-tion and copolymer composition did not depend onthe solvent employed. Without a detailed study, it
can be concluded, however, that points relating tothe terminal model (full points) were displaced
slightly (especially for the f M 2 M 1 M 1 and f M 2 M 1 M 2
triads) when compared to those corresponding to
the penultimate model (blank points). This can be
regarded as an additional proof for the presence of the penultimate unit effect in the discussed mono-
mer systems. This observation is not new. Thetriad distribution versus the copolymer composi-
tion presented by Klumperman and O’Driscoll14
for the copolymerization of STY with maleic an-
hydride in bulk, MEK, and toluene showed com-paratively poor agreement with the terminal
model when compared to the penultimate model.The situation changed dramatically when Set
II of the penultimate-model reactivity ratios (Ta-
ble I) was used for the triad-sequence calculation(Fig. 4). An examination of the discussed copoly-
mers shows that the triad distribution dependedon the solvent used for the copolymerization. The
sequence distribution in the copolymers synthe-sized in toluene was especially different, al-though, as we remember from the previous sec-
tion and Figure 2(a,b), the copolymer-compositioncurves for toluene calculated for both reactivity-
ratio sets (Set I and Set II) overlap precisely.
Note, however, that there is a difference in fitting
the particular triad fractions ( f M 1 M 1 M 1, f M 2 M 1 M 1,
f M 2 M 1 M 2) to the general bootstrap effect rule: tri-
ads involving both monomers M 1 and M 2 lessaccurately fulfill the expectation in terms of thebootstrap effect symptoms.
The results are difficult to interpret from atheoretical point of view. However, the STY-AN
monomer systems in toluene indicated the mostsignificant penultimate unit effect among all the
discussed solvents. The question arises whetherthe observed convergence was coincidental and,therefore, without any physical meaning, or could
be interpreted in terms of the copolymerizationkinetics.
CONCLUSIONS
From this study, it can be concluded that on thebasis of the composition data alone, it is possible
to discriminate between the terminal and penul-timate models for the STY-AN monomer system
under the condition of a very accurate reactivity-ratio determination. The nonlinear approach tothe estimation of reactivity ratios based on the
Nelder and Mead simplex method seems to be a very useful tool for the purpose. The results indi-
cate that the significance of the penultimate uniteffect for a given monomer system can be corre-
lated with an absolute value of the differencebetween the standard deviation of the terminal-
and penultimate-model reactivity ratios. The pen-ultimate unit effect depends on the solvent andseems to be inversely proportional to its polarity.
Contrary to the full equivalence in the represen-tation of the copolymer-composition data with dif-
ferent but numerically equivalent penultimate-model reactivity ratios, the relationship between
the triad-sequence distribution and copolymercomposition does depend on the set of penulti-mate-model reactivity ratios chosen for micro-
structure determination. This observation stillneeds some theoretical interpretation.
This study was supported with 120-501/68-BW-1418/ 18/98 from the Faculty of Chemistry, University of
Warsaw.
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